Summary: Construction of Rational Surfaces
in Projective Fourspace
(joint work with Kristian Ranestad)
Hirotachi Abo
Department of Mathematics
Colorado State University
abo@math.colostate.edu
http://www.math.colostate.edu/abo
August 2005
1. Introduction
P4
:= projective fourspace over C.
Theorem (-, Ranestad, 2004).
There exist five different families of smooth rational
surface in P4
with degree 12 and sectional genus 13.
Remark.
These surfaces are all isomorphic to P2
blown up in
21 points.